In quadrilateral QRTS, we have QR = 11, QS = 9, and ST=2. Sides line RQ and line ST are extended past Q and S, respectively, to meet at point P. If PS = 8 and PQ = 5, then what is RT?
in triangle PQS.
sinP/9 = sinQ/8 = sinS/5
So, you can find angle P
Now, using the law of cosines in triangle PRT
RT^2 = 10^2 + 16^2 - 2*10*16*cos(P)
not sure how I'd do it without trig.
Any clever geometric relationships that make it easy?
To find RT in quadrilateral QRTS, we can use the property that the opposite sides of a quadrilateral are equal in length. Since line RQ and line ST are opposite sides, we can determine the length of ST by subtracting the lengths of QR and PS from the sum of PQ and QS.
1. Start by finding the sum of PQ and QS:
PQ = 5
QS = 9
Sum = PQ + QS = 5 + 9 = 14
2. Subtract the lengths of QR and PS from the sum:
QR = 11
PS = 8
Sum - QR - PS = 14 - 11 - 8 = -5
Since the result is negative, it means that ST is 5 units in length.
3. Now, we need to find RT. Since RT is equal to the opposite side ST, RT is also 5 units in length.
Therefore, RT = 5.